%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : KRS003-1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n024.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Sun Jul 17 03:30:14 EDT 2022

% Result   : Unsatisfiable 0.18s 0.40s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   10
% Syntax   : Number of clauses     :   18 (   5 unt;   0 nHn;  18 RR)
%            Number of literals    :   38 (   0 equ;  25 neg)
%            Maximal clause size   :    4 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    9 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-1 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ c(u)
    | s2least(u) ),
    file('KRS003-1.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ s2least(u)
    | ~ equalish(u1r2(u),u1r1(u)) ),
    file('KRS003-1.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ s2least(u)
    | s(u,u1r1(u)) ),
    file('KRS003-1.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ s2least(u)
    | s(u,u1r2(u)) ),
    file('KRS003-1.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ d(u)
    | s1most(u) ),
    file('KRS003-1.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ s1most(u)
    | ~ s(u,v)
    | ~ s(u,w)
    | equalish(w,v) ),
    file('KRS003-1.p',unknown),
    [] ).

cnf(13,axiom,
    ( ~ e(u)
    | c(u) ),
    file('KRS003-1.p',unknown),
    [] ).

cnf(14,axiom,
    ( ~ f(u)
    | d(u) ),
    file('KRS003-1.p',unknown),
    [] ).

cnf(15,axiom,
    e(exist),
    file('KRS003-1.p',unknown),
    [] ).

cnf(16,axiom,
    f(exist),
    file('KRS003-1.p',unknown),
    [] ).

cnf(17,plain,
    d(exist),
    inference(res,[status(thm),theory(equality)],[16,14]),
    [iquote('0:Res:16.0,14.0')] ).

cnf(18,plain,
    c(exist),
    inference(res,[status(thm),theory(equality)],[15,13]),
    [iquote('0:Res:15.0,13.0')] ).

cnf(43,plain,
    ( ~ s2least(u)
    | ~ s1most(u)
    | ~ s(u,v)
    | equalish(v,u1r1(u)) ),
    inference(res,[status(thm),theory(equality)],[4,9]),
    [iquote('0:Res:4.1,9.1')] ).

cnf(44,plain,
    ( ~ s2least(u)
    | ~ s1most(u)
    | ~ s2least(u)
    | ~ s(u,u1r2(u)) ),
    inference(res,[status(thm),theory(equality)],[43,3]),
    [iquote('0:Res:43.3,3.1')] ).

cnf(45,plain,
    ( ~ s1most(u)
    | ~ s2least(u)
    | ~ s(u,u1r2(u)) ),
    inference(obv,[status(thm),theory(equality)],[44]),
    [iquote('0:Obv:44.0')] ).

cnf(46,plain,
    ( ~ s1most(u)
    | ~ s2least(u) ),
    inference(mrr,[status(thm)],[45,5]),
    [iquote('0:MRR:45.2,5.1')] ).

cnf(47,plain,
    ( ~ d(u)
    | ~ c(u) ),
    inference(ems,[status(thm)],[46,7,1]),
    [iquote('0:EmS:46.0,46.1,7.1,1.1')] ).

cnf(57,plain,
    $false,
    inference(ems,[status(thm)],[47,17,18]),
    [iquote('0:EmS:47.0,47.1,17.0,18.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : KRS003-1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n024.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.33  % CPULimit : 300
% 0.18/0.33  % WCLimit  : 600
% 0.18/0.33  % DateTime : Tue Jun  7 18:59:49 EDT 2022
% 0.18/0.33  % CPUTime  : 
% 0.18/0.40  
% 0.18/0.40  SPASS V 3.9 
% 0.18/0.40  SPASS beiseite: Proof found.
% 0.18/0.40  % SZS status Theorem
% 0.18/0.40  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.18/0.40  SPASS derived 23 clauses, backtracked 0 clauses, performed 0 splits and kept 32 clauses.
% 0.18/0.40  SPASS allocated 75629 KBytes.
% 0.18/0.40  SPASS spent	0:00:00.06 on the problem.
% 0.18/0.40  		0:00:00.03 for the input.
% 0.18/0.40  		0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.40  		0:00:00.00 for inferences.
% 0.18/0.40  		0:00:00.00 for the backtracking.
% 0.18/0.40  		0:00:00.00 for the reduction.
% 0.18/0.40  
% 0.18/0.40  
% 0.18/0.40  Here is a proof with depth 4, length 18 :
% 0.18/0.40  % SZS output start Refutation
% See solution above
% 0.18/0.40  Formulae used in the proof : clause_3 clause_5 clause_6 clause_7 clause_9 clause_11 clause_15 clause_16 clause_1 clause_2
% 0.18/0.40  
%------------------------------------------------------------------------------